About: Dirichlet-multinomial distribution

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In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It i

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rdfs:label	Dirichlet-multinomial distribution (en)
rdfs:comment	In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It i (en)
sameAs	Dirichlet-multinomial distribution Dirichlet-multinomial distribution
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Math dbt:More_footnotes dbt:ProbDistributions dbt:Refbegin dbt:Refend dbt:Reflist dbt:Clarification_needed dbt:Probability_distribution dbt:Peter_Gustav_Lejeune_Dirichlet
Subject	Multivariate discrete distributions Compound probability distributions Discrete distributions
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution?oldid=1060435553&ns=0
Wikipage page ID	9169137 (xsd:integer)
page length (characters) of wiki page	39860 (xsd:nonNegativeInteger)
Wikipage revision ID	1060435553 (xsd:integer)
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has abstract	In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It is frequently encountered in Bayesian statistics, machine learning, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution. It reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily well for large α. The Dirichlet-multinomial is a multivariate extension of the beta-binomial distribution, as the multinomial and Dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution
is rdfs:seeAlso of	Latent Dirichlet allocation
is Wikipage redirect of	Multivariate Polya distribution Dirichlet compound multinomial distribution Multivariate Pólya distribution
is Link from a Wikipage to another Wikipage of	List of statistics articles List of things named after Peter Gustav Lejeune Dirichlet Beta-binomial distribution Categorical distribution Generalized Dirichlet distribution George Pólya Gibbs sampling

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